The Mathematics of Elections. 4/3/08 Tricia Lynn [email protected] Why elections?. Math Awareness Month www.mathaware.org Math and Voting HBO documentary Hacking Democracy Documentary by an activist group called Black Box voting that examined the 2000 Presidential election
Math and Voting
Standard divisor = population ÷ # of representatives
Highest remainders get rounded up
Use modified standard divisor to avoiding rounding
The quota rule states that the number of representatives apportioned to a state is the standard quota or one more than the standard quota.
Population of a state
# of representatives from the state
The absolute unfairness of an apportionment is the absolute value of the difference between the average constituency of state A and the average constituency of state B.
Absolute unfairness of the apportionment
Average constituency of the state receiving the new rep
Each place on the ballot is assigned points. In an election with N candidates, we give 1 point for last place, 2 points for next to last place,…, and N points for first place. The pointed are tallied for each candidate and the candidate with the highest total is the winner. The Borda winner is considered the “compromise candidate.”
In Round 1 of voting, the first place votes for each candidate are counted. If a candidate has a majority of first-place votes, that candidate is the winner.
In rounds 2, 3, 4, et cetera, the names of candidates eliminated from the preference schedule are crossed out and then the first-place votes are recounted. The process is repeated until a candidate has a majority of first-place votes.
This method is similar to a round-robin tournament in which every candidate is matched one-to-one with every other candidate. The candidate that is preferred over the other candidate gets a point in each match up. The candidate with the most points is the winner.
A condorcet candidate is one who wins in every head-to-head comparison against each of the other candidates.
Voting activitists feature in the video clip
Dave Leip’s Atlas of U.S. Presidential Elections
Lots of sample worksheets
Special thanks to Marnie Henneman
Lesson Plan from Mathematics Teacher, January 2000